What is the integral of (10)/(cos(x)-1) ?

The integral of (10)/(cos(x)-1) is 10cot(x/2)+C

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integral of (10)/(cos(x)-1)

\int \frac{10}{cos ( x ) - 1} d x

10 cot (\frac{x}{2}) + C

Solution steps

\int \frac{10}{cos ( x ) - 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int \frac{1}{cos ( x ) - 1} d x

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= 10 \cdot \int - \frac{1}{u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 10 (- (- \frac{1}{u}))

Substitute back

u = tan (\frac{x}{2})

= 10 (- (- \frac{1}{tan ( \frac{x}{2} )}))

Simplify

10 (- (- \frac{1}{tan ( \frac{x}{2} )})) : 10 cot (\frac{x}{2})

= 10 cot (\frac{x}{2})

Add a constant to the solution

= 10 cot (\frac{x}{2}) + C

\frac{d y}{d x} = y x

f (t) = 7 sin (\frac{3 t}{2})

x \to - 1 lim (- x^{2} - 2 x + 3)

(4 x y^{2} - 3) d x + (4 x^{2} y + 4) d y = 0

\frac{d}{d x} (sin (x^{3} + y^{2}))

What is the integral of (10)/(cos(x)-1) ?
The integral of (10)/(cos(x)-1) is 10cot(x/2)+C